Bill takes the commuter train to work every day. During the morning commute, a train arrives every 25 min. If Bill arrives at the station at a random time for the morning commute, what is the probability that he will have to wait at least 5 min for a train?

Let's see if anyone sees the problem with this question that Cengage wrote.

plz stop using the word random without a distribution k thx

03-04-2019, 12:53 PM

Reverend Jones

As much as I'd like to find some reason to chide you for being a stickler, I hate hate hate the ****ty (corporate) textbooks foisted on our students. It's a goddamn crime that we're letting bigcorps feed them glossy **** that forever mucks up their impression of what could have been a simple and straightforward exposition if the author had respected the reader's intelligence _just a little bit_.

But noooo, our high school students get to read all flavors of the **** rainbow of "topic X for people who actually don't want to be forced to think about topic X right now, thxkbye"

03-04-2019, 12:55 PM

Reid

I love teaching math when words like "discrete" pop up and I have only a couple minutes to explain to calculus students what discrete means.

"Well, it's like finite, but not finite, it can be infinite, but infinite where everything is far apart, kind of."

03-04-2019, 12:57 PM

Reverend Jones

So you're teaching freshman or non-majors, because you're literally talking about trying to compensate for them apparently struggling to cope with the need to remember the definition of a word.

03-04-2019, 01:00 PM

Reid

Quote:

Originally Posted by Reverend Jones

As much as I'd like to find some reason to chide you for being a stickler, I hate hate hate the ****ty (corporate) textbooks foisted on our students. It's a goddamn crime that we're letting bigcorps feed them glossy **** that forever mucks up their impression of what could have been a simple and straightforward exposition if the author had respected the reader's intelligence _just a little bit_.

Yeah, pretty much. I really dislike being roped into this textbook.

BTW, this isn't a nitpick. We teach multiple distribution functions, and it's not obvious from the physical layout of the problem that it means a uniform distribution. I mean, if you think about it, people usually wake up at the same time each day and leave around the same time, so you're probably looking more at a normal distribution than a uniform one ~in reality~, not in magic word problem land.

To simply say "uniform distribution" clears up any potential confusion so it should be mentioned.

03-04-2019, 01:00 PM

Reid

Quote:

Originally Posted by Reverend Jones

So you're teaching freshman or non-majors, because you're literally talking about trying to compensate for them apparently struggling to cope with the need to remember the definition of a word.

Yes to both, I teach freshman non-majors calculus.

03-04-2019, 01:02 PM

Reverend Jones

I also think you might be doing it wrong (sorry). Without knowing the context of what you're trying to tell them, I would just make an analogy with bags of beans versus glasses of water.

03-04-2019, 01:11 PM

Reverend Jones

Quote:

Originally Posted by Reid

Yeah, pretty much. I really dislike being roped into this textbook.

BTW, this isn't a nitpick. We teach multiple distribution functions, and it's not obvious from the physical layout of the problem that it means a uniform distribution. I mean, if you think about it, people usually wake up at the same time each day and leave around the same time, so you're probably looking more at a normal distribution than a uniform one ~in reality~, not in magic word problem land.

To simply say "uniform distribution" clears up any potential confusion so it should be mentioned.

I understand, I just hope your students care enough to remember the distinction. The fact that you care makes you a good teacher. My hunch is the textbook authors didn't bother and would prefer to insult their intelligence (rightly or wrongly).

03-04-2019, 01:15 PM

Jon`C

Yo itís like when youíre keeping your side chick a secret from your other side chick

03-04-2019, 01:16 PM

Jon`C

Quote:

Originally Posted by Reverend Jones

I understand, I just hope your students care enough to remember the distinction. The fact that you care makes you a good teacher. My hunch is the textbook authors didn't bother and would prefer to insult their intelligence (rightly or wrongly).

Insulting the readers intelligence is left as an exercise. The proof is trivial.

03-04-2019, 05:06 PM

Reid

Quote:

Originally Posted by Reverend Jones

I also think you might be doing it wrong (sorry). Without knowing the context of what you're trying to tell them, I would just make an analogy with bags of beans versus glasses of water.

Probably a good way to bring it up had I thought of it before lecture. Sometimes it's easy to slip words without realizing the audience.

It was brought up because I'm teaching continuous probability, but to elucidate why we define things the way we do, I show examples from discrete probability where things tend to be more intuitive.

Quote:

Originally Posted by Reverend Jones

I understand, I just hope your students care enough to remember the distinction. The fact that you care makes you a good teacher. My hunch is the textbook authors didn't bother and would prefer to insult their intelligence (rightly or wrongly).

I mean, they'll certainly learn the differences between the distributions because they will be tested on it.

Quote:

Originally Posted by Jon`C

Insulting the readers intelligence is left as an exercise. The proof is trivial.

Yah you know what I'm not even going to try. Students are too dumb clearly.

03-04-2019, 06:35 PM

Reverend Jones

Quote:

Originally Posted by Reid

Probably a good way to bring it up had I thought of it before lecture. Sometimes it's easy to slip words without realizing the audience.

Your explanation might be better in some ways anyway, but mine also works on first graders.

03-04-2019, 10:05 PM

Obi_Kwiet

Quote:

Originally Posted by Jon`C

Or maybe weirdness in mathematics is because our axioms have secret contradictions

Logical positivism was fun while it lasted.

03-04-2019, 11:36 PM

Reverend Jones

Quote:

Originally Posted by Reverend Jones

I would just make an analogy with bags of beans versus glasses of water.

Quote:

Originally Posted by Reverend Jones

Your explanation might be better in some ways anyway, but mine also works on first graders.

That said, it's kinda wrong to say water is continuous rather than discrete... lol. Maybe mention as a postscript that "continuity" of fluids is purely an abstract conception of matter at larger scales.

Then I guess you can start to make them wonder, if matter isn't continuous, is spacetime?? (Maybe this is the fastest route to bootstrap 1st graders into quantum gravity)

03-04-2019, 11:57 PM

Jon`C

AFAIU regular lattice spacetimes have been ruled out, but discrete spacetimes haven’t (although absence of evidence is not evidence of absence). It’s worth noting too that if we do find evidence of discrete space time, it might only be ‘effectively’ discrete at the GCD of discontinuous motions through continuous space. Same thing applies elsewhere. Perhaps the universe permits arbitrary continuous values for electric charges, but it doesn’t provide us any way to create them.

As beings stuck inside this universe, studying the universe using the stuff of the universe, it’s pretty likely that humans will never know for sure what the universe REALLY is.

03-05-2019, 12:00 AM

Reverend Jones

Gramps told me it was made `o tiny `lil strings

03-05-2019, 12:02 AM

Reverend Jones

the universe is a Node.js program posted to hacker news

03-05-2019, 12:03 AM

Jon`C

Obviously it is a simple cellular automaton.

03-05-2019, 12:05 AM

Reverend Jones

Quote:

Originally Posted by Reid

I love teaching math when words like "discrete" pop up and I have only a couple minutes to explain to calculus students what discrete means.

"Well, it's like finite, but not finite, it can be infinite, but infinite where everything is far apart, kind of."

I just realized that Reid had the best explanation all along. He just forgot to draw what he was saying on the blackboard rather than speak it out loud!

I got through about 2 minutes of that rich idiot stammering his way through a Kurzweilian misappropriation of probability before realizing that he doesn't give one **** about the metaphysical argument about simulation, it's just atheist techie prosperity gospel: "the world is a video game because being born into wealth is capitalism's developer console, and the only way I can rationalize my own success is if everybody I exploit is a literal NPC"

**** Elon Musk.

03-05-2019, 02:09 AM

Jon`C

Also, if the universe is a simulation, it's not a ****in' video game. It's probably iterative simulated annealing on a high degree weighted graph.

03-05-2019, 09:37 AM

Reid

I'll never in my life grasp what people even mean by "the universe is a simulation". It's like a categorical error. The universe is just itself, if anything we just discover its laws and principles are much weirder than anyone anticipated.

03-05-2019, 10:14 AM

Reid

It seems like Elon Musk and the primary simulation proponent Nick Bostrum (who Elon Musk seems to be paraphrasing) lie in the same argument: that computer simulation will get so advanced it will be indistinguishable from reality (or, at the least, that it can be). Rofl. Sure once you take this as a given, you can get weird results. But I don't think this claim holds up to any scrutiny.

So they think computers will be able to simulate chemistry? That you can create chemicals nobody has ever seen before and performs experiments which accurately show the results nobody has ever seen before? That it will accurately simulate quantum physics? That it will accurately simulate brain activity?

In doing this we've supposed a computer system exists which contains all possible knowable information about the universe. Because that's what's supposed by it being indistinguishable. Moreover.. this finite system can replicate the entire universe it's in, and moreover that simulated universe has to be capable of running the simulation itself, giving you the potential for unbounded nested simulations.

Okay, right. This is the problem I have with these kinds of thought experiments. The counterfactual of "computer programs indistinguishable from reality" is far-fetched and absurd on inspection. You're getting a GIGO result.

03-05-2019, 11:19 AM

Reid

The weird thing about all of these arguments is that they're often phrased as though a universe like ours is simulating a universe like ours. Once you state it like this, I believe it just falls apart and is basically silly. I guess people really like it because then they can imagine cool video games, but I don't think a thing is possible.

What I believe is accurate is that our universe can simulate a deficient version of our universe. But this is obvious. And if you suppose that then, our universe is the simulation of a universe with laws governing it of a much different nature than ours, beyond comprehension, then what's really been said is "God exists". Which is a fine thing to believe, but if you presuppose a "universe with fundamental laws different from ours", you've described a universe which we can't say anything about but a bit of header information.

03-05-2019, 11:37 AM

Reverend Jones

Quote:

Originally Posted by Reid

So they think computers will be able to simulate chemistry? That you can create chemicals nobody has ever seen before and performs experiments which accurately show the results nobody has ever seen before? That it will accurately simulate quantum physics? That it will accurately simulate brain activity?

I agree Elon Musk is being an idiot here, but my take on his argument is that computers are simulating consciousness, not physical reality. I.e., a program is running that makes experience just plausible enough for its observers (or sole observer, in the case of a solipsistic rich psychopath to play capitalist chess with all us NPCs). Then reality is more like a lucid dream, in the sense that trying to do things that make sense or require consistency or deep thought are being constantly avoided by design, in order to avoid overloading the CPU. This would mean that certain career choices and activities would trigger a "Truman Show" like response from the system, in which it conspires to limit utilization just to keep up, so that circumstances succeed in making you think hard enough about something that needs to be consistent.

If this is the case, then whoever designed such a program spent a hell of a lot of time trying to trick us, because if all they wanted to do was make it into a dream-like experience where we are terrorized away from thinking too hard, they could have been a lot lazier and saved a lot of CPU cycles.

I also think the appeal of the simulation idea comes down to just how mysterious reality actually is.

You see, humans are pretty hardwired to view the world as physical objects which are rigid and have extent. This is confirmed to some degree by infant studies. Infants love to see causation. It's why they love mobiles. They've done studies where they show causation to an infant and then purposefully break it to see how they react. In specific, they show infants videos of balls colliding. Pool balls running into each other. Eventually they replace it with a CG video of one ball rolling into the other, but instead of transferring motion it just stops.

The infants seem to be upset by this video. Infants are constantly developing a causal understanding of the universe which seems predisposed towards classical physical understandings, object permanence, etc.

The issue is that the frontiers of many sciences have pushed to where the idea of physical bodies with extent breaks down. Quantum physics completely throws in the face the notion of physical rigid bodies interacting. It's a completely baffling, strange set of laws that we only comprehend in a rudimentary sense.

Since it's so strange, people seem to have an urge to deny its reality. I genuinely think this is why people start buying into "simulation" arguments. There's a gut feeling that this strangeness can't be real and reality must be something actually simpler, and all we're witnessing is the mistakes of a simulation.

I don't think so. I think reality itself is just far weirder than we're really capable of cognizing. Which is scary and cool.

03-05-2019, 05:50 PM

Obi_Kwiet

Quote:

Originally Posted by Reid

I'll never in my life grasp what people even mean by "the universe is a simulation". It's like a categorical error. The universe is just itself, if anything we just discover its laws and principles are much weirder than anyone anticipated.

Honestly, I think it's just pseudo-profound click bait. I mean, you might be able to conduct a few interesting thought experiments with it, but mostly it's just meaningless and unverifiable speculation. I guess what really annoys me is when people want to assume it's "probably" true and that it somehow arbitrarily justifies some attitude that they want to have.

I mean, if you really want to feel wierded out do some reading and thinking about what consciousness is and how it (maybe) works.

03-06-2019, 05:00 PM

Reid

Quote:

Originally Posted by Obi_Kwiet

Honestly, I think it's just pseudo-profound click bait. I mean, you might be able to conduct a few interesting thought experiments with it, but mostly it's just meaningless and unverifiable speculation. I guess what really annoys me is when people want to assume it's "probably" true and that it somehow arbitrarily justifies some attitude that they want to have.

I mean, if you really want to feel wierded out do some reading and thinking about what consciousness is and how it (maybe) works.

Yeah, it always depends on people making giant scientific advances and so forth too.

And you're right, just pick up any text on the issue by an author and read their argument. Nick Bostrom's argument is interesting per se, even if I think the premises are too shaky to have any serious concern.

For real though: when will people learn that counterfactuals tell you very little? What isn't the case is not very handy to think about.

03-06-2019, 05:04 PM

Reid

So, I presented my students with the phrase "a random number" and I asked why, given their newfound knowledge of distribution/density functions, why this statement is meaningless without context of some function.

Lol, none of them had an answer. Looks like y'all were right about that.

I explained that typically when people ask for a random number between 1 and 10 or whatever, what they mean is a random number with a uniform distribution, and helped work through a version of Cengage's ****ty problem so that they could see what I'm referring to. I think they understood the importance after I made my little stink of it and clarified how the problem is ambiguous.

I didn't have time to go into why there's no uniform distribution on the integers, but that would have been a good example time permitting.

03-06-2019, 07:27 PM

Reverend Jones

Pick a random number between 1 and infinity!

03-20-2019, 12:10 PM

Reid

Quote:

Originally Posted by Reverend Jones

Pick a random number between 1 and infinity!

Yeahhhhh just roll an ∞-sided dice!

One of my favorite parts of teaching calculus is when students are fine with everything about a concept except for the most rudimentary ideas. We gave them an equation where we said a probability density function f(x)=ax^2+bx has expected value 0.6 (0,6 for the communists), find a and b. They were able to set up and solve the integral just fine, but then had one equation with two variables.

They were like whaaat do I do? So I said, "Think really hard back to 8th grade, you have one equation and two unknowns. What do you need to solve for two unknowns?" After a bit of mental rummaging, they realized they need two equations. They were quick to pick up on that f(x) being a PDF means its integral should be one, so they had their two equations and two unknowns. Then they couldn't figure out how to find where two lines intersect..

I swear, something about the middle school brain is a mushy pit where no math sticks. It's interesting how few people end up remembering these kinds of elementary ideas when they're clearly capable of it.

03-20-2019, 12:12 PM

Reid

TBH it's probably doesn't help that the caliber of middle school math teachers has to be pretty low. I have no evidence, but this feels like one of those claims that feels so right it has to be true.

03-30-2019, 02:40 PM

Reid

Fun fact: the discovery of logarithms only predates the discovery of calculus by about 60 years.

04-02-2019, 10:11 AM

Reid

What sort of sicko adds autcompleting parentheses to their environment? I don't get people who overuse "features"

04-02-2019, 10:13 AM

Jon`C

Lisp programmers?

04-02-2019, 11:03 AM

Reverend Jones

Lisp programmers would also probably call the syntax of your language an overused feature.